P is 3. The conditions require testing permutations of digits 1-5 where P < Q, S > P > T, and R < T, which only works when P=3.​​

Problem Breakdown

A five-digit number PQRST uses distinct digits 1 through 5. The inequalities P < Q, S > P > T, and R < T must hold.​

Valid Permutations

Only two arrangements satisfy all conditions:

• 34152 (P=3, Q=4, R=1, S=5, T=2): 3<4, 5>3>2, 1<2.

• 35142 (P=3, Q=5, R=1, S=4, T=2): 3<5, 4>3>2, 1<2.​

Option Analysis

• (A) 1: Fails as no valid number starts with 1 (T must be <1 impossible; S>P=1 limits options).​

• (B) 2: Fails (e.g., attempts like 2_1_5_? violate distinctness or S>P> T).​

• (C) 3: Correct, as shown in both valid cases.​

• (D) 4: Fails (P=4 requires T<4, but no fitting Q,S,R from remaining digits).​

The five-digit number PQRST distinct digits 1-5 puzzle challenges logical reasoning skills vital for CSIR NET Life Sciences and competitive exams. This problem requires finding the unique value of P satisfying P < Q, S > P > T, and R < T using permutations of {1,2,3,4,5}.​

Step-by-Step Solution

Exhaustive checking of 120 permutations yields only two valid numbers: 34152 and 35142. Both have P=3, confirming the answer.​

Key constraints narrow possibilities:

• T ∈ {2,3,4} (since P > T ≥1 and S > P ≤5).

• R < T and distinct from others.​

Why P=3 Only?

Higher P=4 or 5 leaves insufficient larger digits for S > P. Lower P=1 or 2 fails R < T or distinctness. CSIR NET aspirants benefit from this permutation logic for quant sections.​

Exam Tips

Practice similar five-digit number PQRST puzzles to boost speed. Code verification ensures accuracy over manual enumeration.​